Finite Group Databasebeta

← C2×#13080161 #15628791

Subgroups — C2×#13080161 #15628791

Order 2816.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic, complemented
2C22×#66957C211yesmaximal, characteristic, complemented
3C2×#10623084C211yesmaximal, characteristic, complemented
4C2×#10623081C211yesmaximal, characteristic, complemented
5#13080161C2116yesmaximal, direct product factor
6C2×#10622325C211yesmaximal, characteristic, complemented
7C2×#10622747C211yesmaximal, characteristic, complemented
8C2×#10622728C211yesmaximal, characteristic, complemented
9C2×#10622458C211yesmaximal, characteristic, complemented
10C2×#10622456C211yesmaximal, characteristic, complemented
11C2×#10622346C211yesmaximal, characteristic, complemented
12C2×#10622347C211yesmaximal, characteristic, complemented
13C2×#10622347C211yesmaximal, characteristic, complemented
14C2×#10622345C211yesmaximal, characteristic, complemented
15C2×#10622323C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C22×#4339C2211yescharacteristic
19C22×#4339C2211yescharacteristic, complemented
20C23×D44C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C23×C8×C11C2211yescharacteristic, complemented
23C2×C4×D4×C11C2211yescharacteristic
24C2×#66993—21no—
25C2×#66990—21no—
26C2×#66983C2211yescharacteristic
27C2×#66983C2211yescharacteristic
28C2×#66983C2211yescharacteristic, complemented
29C2×#66977C2211yescharacteristic
30C2×#66961—28no—
31C2×#66961C2218yescomplemented
32C22×Dic44C2211yescharacteristic, complemented
33C2×#66957—28no—
34C2×#66957C2218yescomplemented
35C22×D88C2211yescharacteristic
36C22×D88C2211yescharacteristic
37C22×D88C2211yescharacteristic
38C22×D88C2211yescharacteristic
39C22×#4314C2211yescharacteristic
40C22×#4314C2211yescharacteristic
41C22×#4314C2211yescharacteristic, complemented
42C22×#4314C2211yescharacteristic, complemented
43#10623084—24no—
44#10623084C2218yescomplemented
45#10623081—24no—
46#10623081C2218yescomplemented
47C2×#66947—21no—
48C2×#66946—21no—
49C2×#66937—21no—
50C2×#66937—21no—
51C2×#66937—21no—
52C2×C22⋊C4×D11—21no—
53C2×#66928C2211yescharacteristic
54C2×#66927C2211yescharacteristic, complemented
55C2×C4×D44C2211yescharacteristic
56C2×C4×Dic22C2211yescharacteristic, complemented
57C11×#435C2218yescomplemented
58C2×C11×C4⋊C8C2211yescharacteristic, complemented
59C2×C11×C22⋊C8C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic, complemented
61C2×C11×#97C2211yescharacteristic, complemented
62#10622747C2218yescomplemented
63#10622728C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66885C2211yescharacteristic
66C2×#66885C2211yescharacteristic, complemented
67C2×#66885C2211yescharacteristic, complemented
68C2×#66882C2211yescharacteristic, complemented
69C2×#66880C2211yescharacteristic, complemented
70C2×#66880C2211yescharacteristic, complemented
71#10622458C2218yescomplemented
72#10622456C2218yescomplemented
73#10622347C2218yescomplemented
74#10622347C2218yescomplemented
75#10622346C2218yescomplemented
76#10622345C2218yescomplemented
77#10622325C2218yescomplemented
78#10622323C2218yescomplemented
79C24×D11—21no—
80C22×D4×C11D411yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C2×#4339—22no—
90C2×#4339—22no—
91C2×#4339—22no—
92C2×#4339—24no—
93C2×#4339—24no—
94C2×#4339—24no—
95C2×#4339—42no—
96C2×#4339—42no—
97C2×#4339—42no—
98C2×#4339C2314yes—
99C2×#4339C2314yes—
100C2×#4339C2314yescomplemented
101C22×D44—24no—
102C22×D44—21no—
103C22×D44—21no—
104C22×D44—22no—
105C22×D44—21no—
106C22×D44—42no—
107C22×D44C2311yescharacteristic
108C22×D44C2311yescharacteristic
109C22×D44C2311yescharacteristic
110C22×D44C2314yes—
111C22×D44C2311yescharacteristic
112C22×C4×D11—21no—
113C22×C4×D11—21no—
114C22×C4×D11—21no—
115C22×C4×D11—21no—
116C22×Dic22C2311yescharacteristic
117C22×Dic22C2311yescharacteristic
118C2×C11×M16—24no—
119C2×C11×M16C2314yes—
120C22×C8×C11—24no—
121C22×C8×C11C2311yescharacteristic
122C22×C8×C11C2311yescharacteristic
123C22×C8×C11C2311yescharacteristic
124C22×C8×C11C2311yescharacteristic
125C22×C8×C11C2314yescomplemented
126C4×D4×C11D414yes—
127C4×D4×C11C2314yes—
128C2×C11×C4⋊C4D411yescharacteristic
129C2×C11×C22⋊C4D411yescharacteristic
130C2×C11×C22⋊C4D411yescharacteristic
131C2×C42×C11C2311yescharacteristic
132C2×C22⋊Dic11—21no—
133#66993—28no—
134#66990—28no—
135#66983—22no—
136#66983—22no—
137#66983—22no—
138#66983C2314yes—
139#66983C2314yes—
140#66983C2314yescomplemented
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149#66977—22no—
150#66977C2314yes—
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4—21no—
153C2×C4×Dic11—21no—
154#66961—232no—
155C2×Dic44—24no—
156C2×Dic44C2314yescomplemented
157#66957—232no—
158C2×D88—24no—
159C2×D88—24no—
160C2×D88—24no—
161C2×D88—42no—
162C2×D88C2314yes—
163C2×D88C2314yes—
164C2×D88C2314yes—
165C2×D88C2314yes—
166C2×#4314—24no—
167C2×#4314—24no—
168C2×#4314—42no—
169C2×#4314D418yescomplemented
170C2×#4314C2314yes—
171C2×#4314C2314yes—
172C2×#4314C2314yescomplemented
173C2×#4314C2314yescomplemented
174#66947—28no—
175#66946—28no—
176#66937—28no—
177#66937—28no—
178#66937—28no—
179C22⋊C4×D11—28no—
180#66928—22no—
181#66928C2314yes—
182#66927—22no—
183#66927C2314yescomplemented
184C4×D44—22no—
185C4×D44C2314yes—
186C4×Dic22—22no—
187C4×Dic22C2314yescomplemented
188C11×C4⋊C8C2314yescomplemented
189C11×C22⋊C8C2314yes—
190C11×C22⋊C8C2314yescomplemented
191C11×#97C2314yescomplemented
192#66885C2314yes—
193#66885C2314yes—
194#66885C2314yescomplemented
195#66885C2314yescomplemented
196#66882C2314yescomplemented
197#66880C2314yescomplemented
198#66880C2314yescomplemented
199C2×#3268—111nomaximal, Sylow
200C24×C11C2×D411yescharacteristic
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—24no—
207C23×D11—44no—
208C23×D11—44no—
209C23×D11—82no—
210C2×D4×C11—42no—
211C2×D4×C11C2×D414yes—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2411yescharacteristic
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—24no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—82no—
235C2×C22⋊D11—82no—
236C2×C22⋊D11—82no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—21no—
241#4339—28no—
242#4339—28no—
243#4339—28no—
244#4339—44no—
245#4339—44no—
246#4339—44no—
247#4339—48no—
248#4339—48no—
249#4339—48no—
250C2×D44—28no—
251C2×D44—21no—
252C2×D44—21no—
253C2×D44—21no—
254C2×D44—24no—
255C2×D44—21no—
256C2×D44—24no—
257C2×D44—24no—
258C2×D44—22no—
259C2×D44—22no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44—22no—
263C2×D44—22no—
264C2×D44—22no—
265C2×D44—44no—
266C2×D44—44no—
267C2×D44—48no—
268C2×D44—44no—
269C2×D44—82no—
270C2×D44C2×D414yes—
271C2×D44C2412yes—
272C2×D44C2412yes—
273C2×D44C2412yes—
274C2×D44C2412yes—
275C2×C4×D11—24no—
276C2×C4×D11—24no—
277C2×C4×D11—24no—
278C2×C4×D11—24no—
279C2×C4×D11—44no—
280C2×C4×D11—44no—
281C2×C4×D11—44no—
282C2×C4×D11—82no—
283C2×Dic22—21no—
284C2×Dic22—22no—
285C2×Dic22—21no—
286C2×Dic22—22no—
287C2×Dic22—22no—
288C2×Dic22C2×D414yes—
289C2×Dic22C2412yes—
290C2×Dic22C2412yes—
291C11×M16—28no—
292C2×C8×C11—28no—
293C2×C8×C11—22no—
294C2×C8×C11—22no—
295C2×C8×C11—22no—
296C2×C8×C11C2×D414yes—
297C2×C8×C11C2412yes—
298C2×C8×C11C2412yes—
299C2×C8×C11C2412yes—
300C2×C8×C11C2412yes—
301C11×C4⋊C4C2×D414yes—
302C11×C22⋊C4C2×D414yes—
303C11×C22⋊C4C2×D414yes—
304C42×C11C2×D412yes—
305C42×C11C2412yes—
306C22⋊Dic11—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4—24no—
313C4⋊Dic11—21no—
314C4⋊Dic11—21no—
315C4⋊Dic11C2412yes—
316C4⋊Dic11C2412yes—
317Dic11⋊C4—24no—
318Dic11⋊C4—24no—
319C4×Dic11—24no—
320Dic44—28no—
321D88—28no—
322D88—28no—
323D88—28no—
324D88—44no—
325#4314—28no—
326#4314—28no—
327#4314—44no—
328#4314C2×D4116yescomplemented
329C22×AGL(1,ℤ/8)—111no—
330C22×#135—111no—
331C2×#550—111no—
332C2×#546—111no—
333#3268—1116no—
334C2×#496—111no—
335C2×#468—111no—
336C2×#466—111no—
337C2×#464—111no—
338C2×#459—111no—
339C2×#452—111no—
340C2×#449—111no—
341C2×#449—111no—
342C2×#447—111no—
343C2×#440—111no—
344C2×#435D1111yescharacteristic, complemented
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11C22×D412yes—
352C23×C11C22×D412yes—
353C23×C11C22×D411yescharacteristic
354C22×D11—24no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—48no—
360C22×D11—42no—
361C22×D11—42no—
362C22×D11—48no—
363C22×D11—42no—
364C22×D11—42no—
365C22×D11—42no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—42no—
371C22×D11—42no—
372C22×D11—84no—
373C22×D11—816no—
374D4×C11—44no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—24no—
380C2×C4×C11—24no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11C22×D412yes—
386C2×C4×C11C22×D412yes—
387C2×C4×C11C22×D412yes—
388C2×C4×C11C22×D412yes—
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D412yes—
391C2×C4×C11H(5,𝔽2)12yes—
392C2×C4×C11C2511yescharacteristic
393C22⋊D11—48no—
394C22⋊D11—48no—
395C22⋊D11—48no—
396C22⋊D11—84no—
397C22⋊D11—84no—
398C22⋊D11—84no—
399C2×Dic11—24no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—42no—
405C2×Dic11—42no—
406C2×Dic11—42no—
407D44—24no—
408D44—22no—
409D44—22no—
410D44—22no—
411D44—22no—
412D44—22no—
413D44—22no—
414D44—22no—
415D44—48no—
416D44—48no—
417D44—42no—
418D44—42no—
419D44—42no—
420D44—84no—
421D44C22×D414yes—
422C4×D11—48no—
423C4×D11—48no—
424C4×D11—48no—
425C4×D11—84no—
426Dic22—24no—
427Dic22—22no—
428Dic22—22no—
429Dic22—22no—
430Dic22—42no—
431Dic22C22×D414yes—
432C8×C11—22no—
433C8×C11—22no—
434C8×C11—22no—
435C8×C11C22×D414yes—
436C22×#41—111no—
437C22×#41—111no—
438C22×#41—111no—
439C23×D4—111no—
440C2×AGL(1,ℤ/8)—118no—
441C2×AGL(1,ℤ/8)—228no—
442C2×#135—118no—
443C2×#135—228no—
444C22×Q16—111no—
445C22×SD16—111no—
446C22×SD16—111no—
447C22×SD16—111no—
448C22×SD16—111no—
449C22×D8—111no—
450C22×D8—111no—
451C22×D8—111no—
452C22×D8—111no—
453C22×M16C2×D1111yescharacteristic
454C23×C8C2×D1111yescharacteristic, complemented
455#550—118no—
456#550—224no—
457#546—118no—
458#546—224no—
459C2×#127—111no—
460C2×#127—221no—
461C2×#124—111no—
462C2×#123—221no—
463C2×C22⋊Q8—111no—
464C2×#121—111no—
465C2×#121—111no—
466C2×#121—111no—
467C2×#121—221no—
468C2×#121—221no—
469C2×#121—221no—
470C2×#120—221no—
471C2×C4×Q8—111no—
472C2×C4×D4—111no—
473C2×C4×D4—221no—
474C2×C4×D4C2×D1111yescharacteristic
475C22×C22⋊C4—221no—
476#496—118no—
477#468—118no—
478#466—118no—
479#464—118no—
480#459—118no—
481#452—118no—
482#449—118no—
483#449—118no—
484#447—118no—
485#440—118no—
486#435C2×D1118yescomplemented
487C2×#107—111no—
488C2×C4⋊C8C2×D1111yescharacteristic, complemented
489C2×#103—111no—
490C2×#103—111no—
491C2×#102—111no—
492C2×#102—111no—
493C2×#102—111no—
494C2×#102—111no—
495C2×C22⋊C8C2×D1111yescharacteristic
496C2×C22⋊C8C2×D1111yescharacteristic, complemented
497C2×#97C2×D1111yescharacteristic, complemented
498C22×C11—22no—
499C22×C11—22no—
500C22×C11—22no—
501C22×C11—22no—
502C22×C11—22no—
503C22×C11—22no—
504C22×C11—44no—
505C22×C11—44no—
506C22×C11D4212yes—
507C22×C11#57512yes—
508C22×C11#57612yes—
509C22×C11C23×D411yescharacteristic
510C2×D11—24no—
511C2×D11—48no—
512C2×D11—42no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—816no—
524C2×D11—84no—
525C2×D11—84no—
526C2×D11—84no—
527C4×C11—22no—
528C4×C11—22no—
529C4×C11—22no—
530C4×C11—22no—
531C4×C11D4212yes—
532C4×C11C23×D411yescharacteristic
533C4×C11C2×H(5,𝔽2)11yescharacteristic
534Dic11—24no—
535Dic11—42no—
536Dic11—42no—
537Dic11—42no—
538C25—221no—
539C2×#41—114no—
540C2×#41—114no—
541C2×#41—114no—
542C2×#41—224no—
543C2×#41—224no—
544C2×#41—224no—
545C2×#41—222no—
546C2×#41—222no—
547C2×#41—222no—
548C2×#41—442no—
549C2×#41—442no—
550C2×#41—442no—
551C22×Q8—111no—
552C22×Q8—111no—
553C22×D4—111no—
554C22×D4—111no—
555C22×D4—111no—
556C22×D4—111no—
557C22×D4—114no—
558C22×D4—224no—
559C22×D4—221no—
560C22×D4—221no—
561C22×D4—221no—
562C22×D4—221no—
563C22×D4—221no—
564C22×D4—221no—
565C22×D4—221no—
566C22×D4—221no—
567C22×D4—222no—
568C22×D4—221no—
569C22×D4—442no—
570C22×D4D4411yescharacteristic
571C23×C4—221no—
572C23×C4—221no—
573C23×C4—221no—
574C23×C4—221no—
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577AGL(1,ℤ/8)—2232no—
578#135—2232no—
579C2×Q16—114no—
580C2×Q16—224no—
581C2×SD16—118no—
582C2×SD16—114no—
583C2×SD16—114no—
584C2×SD16—114no—
585C2×SD16—114no—
586C2×SD16—224no—
587C2×SD16—224no—
588C2×SD16—442no—
589C2×D8—114no—
590C2×D8—114no—
591C2×D8—114no—
592C2×D8—114no—
593C2×D8—224no—
594C2×D8—224no—
595C2×D8—224no—
596C2×D8—442no—
597C2×M16—24no—
598C2×M16C22×D1114yes—
599C22×C8—24no—
600C22×C8C22×D1111yescharacteristic
601C22×C8C22×D1111yescharacteristic
602C22×C8C22×D1111yescharacteristic
603C22×C8C22×D1111yescharacteristic
604C22×C8C22×D1114yescomplemented
605#127—114no—
606#127—228no—
607#127—222no—
608#124—114no—
609#124—222no—
610#123—228no—
611C22⋊Q8—114no—
612C22⋊Q8—222no—
613#121—114no—
614#121—114no—
615#121—114no—
616#121—222no—
617#121—222no—
618#121—222no—
619#121—228no—
620#121—228no—
621#121—228no—
622#120—228no—
623C4×Q8—114no—
624C4×Q8—222no—
625C4×D4—114no—
626C4×D4—228no—
627C4×D4—222no—
628C4×D4D4414yes—
629C4×D4C22×D1114yes—
630C2×C4⋊C4—111no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—221no—
633C2×C4⋊C4—221no—
634C2×C4⋊C4D4411yescharacteristic
635C2×C22⋊C4—221no—
636C2×C22⋊C4—221no—
637C2×C22⋊C4—221no—
638C2×C22⋊C4—221no—
639C2×C22⋊C4—221no—
640C2×C22⋊C4—221no—
641C2×C22⋊C4—221no—
642C2×C22⋊C4—228no—
643C2×C22⋊C4D4411yescharacteristic
644C2×C22⋊C4D4411yescharacteristic
645C2×C42—221no—
646C2×C42C22×D1111yescharacteristic
647#107—114no—
648C4⋊C8C22×D1114yescomplemented
649#103—114no—
650#103—114no—
651#102—114no—
652#102—114no—
653#102—114no—
654#102—114no—
655C22⋊C8C22×D1114yes—
656C22⋊C8C22×D1114yescomplemented
657#97C22×D1114yescomplemented
658C2×C11—42no—
659C2×C11—42no—
660C2×C11#326814yescomplemented
661C2×C11C2×D4211yescharacteristic
662C2×C11C2×#57511yescharacteristic
663C2×C11C2×#57611yescharacteristic
664D11—44no—
665D11—82no—
666D11—82no—
667D11—82no—
668C24—221no—
669C24—221no—
670C24—221no—
671C24—221no—
672C24—224no—
673C24—444no—
674C24—444no—
675C24—882no—
676C24C2×D4411yescharacteristic
677C24C2×D4411yescharacteristic
678#41—228no—
679#41—228no—
680#41—228no—
681#41—444no—
682#41—444no—
683#41—444no—
684#41—448no—
685#41—448no—
686#41—448no—
687C2×Q8—114no—
688C2×Q8—112no—
689C2×Q8—112no—
690C2×Q8—221no—
691C2×Q8—221no—
692C2×Q8—222no—
693C2×Q8—222no—
694C2×Q8—222no—
695C2×D4—42no—
696C2×D4—114no—
697C2×D4—112no—
698C2×D4—112no—
699C2×D4—112no—
700C2×D4—112no—
701C2×D4—228no—
702C2×D4—224no—
703C2×D4—224no—
704C2×D4—224no—
705C2×D4—224no—
706C2×D4—224no—
707C2×D4—224no—
708C2×D4—221no—
709C2×D4—224no—
710C2×D4—224no—
711C2×D4—221no—
712C2×D4—221no—
713C2×D4—221no—
714C2×D4—224no—
715C2×D4—222no—
716C2×D4—222no—
717C2×D4—222no—
718C2×D4—222no—
719C2×D4—222no—
720C2×D4—222no—
721C2×D4—222no—
722C2×D4—444no—
723C2×D4—448no—
724C2×D4—444no—
725C2×D4—444no—
726C2×D4—444no—
727C2×D4—444no—
728C2×D4—444no—
729C2×D4—882no—
730C2×D4—882no—
731C2×D4—882no—
732C2×D4—882no—
733C2×D4C2×D4414yes—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—224no—
743C22×C4—224no—
744C22×C4—224no—
745C22×C4—224no—
746C22×C4—444no—
747C22×C4—444no—
748C22×C4—444no—
749C22×C4—882no—
750C22×C4C2×D4412yes—
751C22×C4C2×D4412yes—
752C22×C4C2×D4411yescharacteristic
753C22×C4C2×D4411yescharacteristic
754C22×C4C2×D4411yescharacteristic
755C22×C4C2×D4411yescharacteristic
756C22×C4C23×D1112yes—
757C22×C4C23×D1112yes—
758C22×C4C23×D1111yescharacteristic
759Q16—228no—
760SD16—1116no—
761SD16—228no—
762SD16—228no—
763SD16—444no—
764D8—228no—
765D8—228no—
766D8—228no—
767D8—444no—
768M16—28no—
769C2×C8—22no—
770C2×C8—22no—
771C2×C8—22no—
772C2×C8—28no—
773C2×C8D4×D1114yes—
774C2×C8C23×D1112yes—
775C2×C8C23×D1112yes—
776C2×C8C23×D1112yes—
777C2×C8C23×D1112yes—
778C4⋊C4—112no—
779C4⋊C4—112no—
780C4⋊C4—221no—
781C4⋊C4—221no—
782C4⋊C4—224no—
783C4⋊C4—224no—
784C4⋊C4C2×D4414yes—
785C22⋊C4—224no—
786C22⋊C4—224no—
787C22⋊C4—224no—
788C22⋊C4—224no—
789C22⋊C4—224no—
790C22⋊C4—224no—
791C22⋊C4—224no—
792C22⋊C4C2×D4414yes—
793C22⋊C4C2×D4414yes—
794C42—224no—
795C42C2×D4412yes—
796C42C23×D1112yes—
797C11C2×#326811yescharacteristic, complemented, Sylow
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—224no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—448no—
810C23—448no—
811C23—442no—
812C23—442no—
813C23—442no—
814C23—442no—
815C23—442no—
816C23—442no—
817C23—442no—
818C23—442no—
819C23—442no—
820C23—442no—
821C23—442no—
822C23—884no—
823C23—8816no—
824C23C22×D4412yes—
825C23C22×D4412yes—
826C23C22×D4411yescharacteristic
827Q8—114no—
828Q8—224no—
829Q8—222no—
830Q8—222no—
831Q8—222no—
832Q8—442no—
833D4—44no—
834D4—114no—
835D4—224no—
836D4—222no—
837D4—222no—
838D4—222no—
839D4—222no—
840D4—222no—
841D4—222no—
842D4—222no—
843D4—448no—
844D4—448no—
845D4—448no—
846D4—448no—
847D4—448no—
848D4—442no—
849D4—442no—
850D4—442no—
851D4—884no—
852D4—884no—
853D4—884no—
854D4—884no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—224no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—448no—
871C2×C4—448no—
872C2×C4—448no—
873C2×C4—442no—
874C2×C4—442no—
875C2×C4—442no—
876C2×C4—884no—
877C2×C4C22×D4412yes—
878C2×C4C22×D4412yes—
879C2×C4C22×D4412yes—
880C2×C4C22×D4412yes—
881C2×C4C22×D4411yescharacteristic
882C2×C4C2×D4×D1112yes—
883C2×C4#6704212yes—
884C2×C4C24×D1111yescharacteristic
885C8—22no—
886C8—22no—
887C8—22no—
888C8C2×D4×D1114yes—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—44no—
896C22—44no—
897C22—224no—
898C22—448no—
899C22—442no—
900C22—442no—
901C22—442no—
902C22—442no—
903C22—442no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—8816no—
911C22—884no—
912C22—884no—
913C22—884no—
914C22D4×D4412yes—
915C22#1062327912yes—
916C22#1062328312yes—
917C22C23×D4411yescharacteristic
918C4—22no—
919C4—22no—
920C4—22no—
921C4—22no—
922C4—224no—
923C4—442no—
924C4—442no—
925C4—442no—
926C4D4×D4412yes—
927C4C22×D4×D1111yescharacteristic
928C4C2×#6704211yescharacteristic
929C2—42no—
930C2—42no—
931C2—444no—
932C2—882no—
933C2—882no—
934C2—882no—
935C2#1308016114yesdirect product factor
936C2C2×D4×D4411yescharacteristic
937C2C2×#1062327911yescharacteristic
938C2C2×#1062328311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
hypercenterC2×#435D11
hypocenterC11C2×#3268
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#66961C2semidirect
2. C22×#66957C2semidirect
3. C2×#10623084C2semidirect
4. C2×#10623081C2semidirect
5. #13080161C2direct (N × H)
6. C2×#10622325C2semidirect
7. C2×#10622747C2semidirect
8. C2×#10622728C2semidirect
9. C2×#10622458C2semidirect
10. C2×#10622456C2semidirect
11. C2×#10622346C2semidirect
12. C2×#10622347C2semidirect
13. C2×#10622347C2semidirect
14. C2×#10622345C2semidirect
15. C2×#10622323C2semidirect
16. C2×C11×#435C2semidirect
19. C22×#4339C22semidirect
22. C23×C8×C11C22semidirect
28. C2×#66983C22semidirect
31. C2×#66961C22semidirect
32. C22×Dic44C22semidirect
34. C2×#66957C22semidirect
41. C22×#4314C22semidirect
42. C22×#4314C22semidirect
44. #10623084C22semidirect
46. #10623081C22semidirect
54. C2×#66927C22semidirect
56. C2×C4×Dic22C22semidirect
57. C11×#435C22semidirect
58. C2×C11×C4⋊C8C22semidirect
60. C2×C11×C22⋊C8C22semidirect
61. C2×C11×#97C22semidirect
62. #10622747C22semidirect
63. #10622728C22semidirect
66. C2×#66885C22semidirect
67. C2×#66885C22semidirect
68. C2×#66882C22semidirect
69. C2×#66880C22semidirect
70. C2×#66880C22semidirect
71. #10622458C22semidirect
72. #10622456C22semidirect
73. #10622347C22semidirect
74. #10622347C22semidirect
75. #10622346C22semidirect
76. #10622345C22semidirect
77. #10622325C22semidirect
78. #10622323C22semidirect
100. C2×#4339C23semidirect
125. C22×C8×C11C23semidirect
140. #66983C23semidirect
156. C2×Dic44C23semidirect
169. C2×#4314D4semidirect
172. C2×#4314C23semidirect
173. C2×#4314C23semidirect
183. #66927C23semidirect
187. C4×Dic22C23semidirect
188. C11×C4⋊C8C23semidirect
190. C11×C22⋊C8C23semidirect
191. C11×#97C23semidirect
194. #66885C23semidirect
195. #66885C23semidirect
196. #66882C23semidirect
197. #66880C23semidirect
198. #66880C23semidirect
328. #4314C2×D4semidirect
344. C2×#435D11semidirect
454. C23×C8C2×D11semidirect
486. #435C2×D11semidirect
488. C2×C4⋊C8C2×D11semidirect
496. C2×C22⋊C8C2×D11semidirect
497. C2×#97C2×D11semidirect
604. C22×C8C22×D11semidirect
648. C4⋊C8C22×D11semidirect
656. C22⋊C8C22×D11semidirect
657. #97C22×D11semidirect
660. C2×C11#3268semidirect
797. C11C2×#3268semidirect
935. C2#13080161direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#669612
C22×#669572
C2×#106230842
C2×#106230812
#130801612
C2×#106223252
C2×#106227472
C2×#106227282
C2×#106224582
C2×#106224562
C2×#106223462
C2×#106223472
C2×#106223452
C2×#106223232
C2×C11×#4352
C2×#326811